pubs.acs.org/Langmuir © 2011 American Chemical Society
Obtaining Charge Distributions on Geometrically Generic Nanostructures Using Scanning Force Microscopy Keith E. Jarmusik,† Steven J. Eppell,*,† Daniel J. Lacks,‡ and Fredy R. Zypman*,§ †
Department of Biomedical Engineering, and ‡Department of Chemical Engineering, Case Western Reserve University, Cleveland, Ohio 44106, United States, and §Yeshiva University, Departments of Physics, New York, New York 10033, United States Received October 15, 2010. Revised Manuscript Received December 15, 2010 We develop the self-consistent sum of dipoles (SCSD) theory for the purpose of recovering charge densities present on nanostructures using scanning force microscope (SFM) force-separation experiments. The dielectric probe is discretized into volume elements characterized by their atomic polarizabilities. Magnitudes of the induced dipole in each element are calculated based on discrete charges placed on the surfaces, dipole-dipole interactions, and dielectric and ionic properties of the surrounding medium. We perform two model-model comparisons, one with a macroscopic dielectric sphere and one with a nanocluster of silicon atoms. In both cases, using a single adjustable parameter, our SCSD theory agrees with the accepted theories to better than 99%. Force-separation curves between a silicon nitride probe and the basal plane of highly oriented pyrolytic graphite in nine ionic concentration and pH combinations were fit with a root-mean-square error of 3.6 pN, an improvement over the 12 pN error obtained using the Derjaguin approximation. These results suggest that the SCSD will be useful in modeling SFM force-separation data to obtain spatially varying charge densities on surfaces with complex geometries.
I. Introduction Designing self-assembled structures and understanding behavior of naturally occurring materials requires an ability to model the properties of these systems at the nanoscale. Substantial progress has been made in developing theories to do this.1 All such theories require input of experimentally obtained physical parameters such as electronic charge, polarizability, modulus, and persistence length. Experimental determination of these parameters is currently a bottleneck in making full use of the existing theories. A thrust of our group is development of the scanning force microscope (SFM) to measure local electrostatic constitutive parameters of nanoscale objects.2-5 The most common form of this technique is often referred to as electrostatic force microscopy (ESFM) when the dominant force in the measurement is electrostatic.6 ESFM experiments generally assume a charge on the SFM tip as well as charges on the surface. A signature of our efforts is to create a system where the charge on the tip is as near neutral as possible. This has the effect of minimizing the electrostatic footprint of the SFM tip on the sample, thus maximizing the measurement’s resolution. In addition, it minimizes the 1/r2 force which may act to rearrange or translate surface resident molecules prior to the arrival of the SFM tip to the surface. Our goal is to make electrostatic measurements on biological molecules whose charge densities and conformations change in response to variations in ambient pH and ionic strength. To obtain the data we seek, the measurements must be made near physiologic pH and ionic concentration. These conditions present challenges when using standard SFM methods *To whom correspondence should be addressed. (1) Bishop, K. J. M.; Wilmer, C. E.; Soh, S.; Grzybowski, B. A. Small 2009, 5, 1600–1630. (2) Eppell, S. J.; Todd, B. A.; Zypman, F. R. Improved algorithm to extract force-distance curves from scanning force microscope data. Materials Issues and Modeling for Device Nanofabrication, 2000, 584, 189-194. (3) Eppell, S. J.; Zypman, F. R.; Marchant, R. E. Langmuir 1993, 9, 2281–2288. (4) Zypman, F. R.; Eppell, S. J. Scanning force microscope to determine interaction forces with high-frequency cantilever. U.S. Patent 6,452,170, September 17, 2002. (5) Zypman, F. R.; Eppell, S. J. J. Vac. Sci. Technol., B 1997, 15, 1853–1860. (6) Colchero, J.; Gil, A.; Baro, A. M. Phys. Rev. B 2001, 64, 245403.
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of data collection and analysis. At physiologic ion concentrations, the energy density of the electric field generated by the molecules is greater than that of the thermal bath only within a few nanometers above the surface. At such small tip-sample separations, typical SFM cantilevers used in fluid exhibit a snap-to-contact instability requiring extraction of force data while the SFM tip is not at equilibrium. In addition, since the measurements must be made in fluid, the quality factor of the SFM cantilever is too low (
